A) \[\lambda \]is less than \[\frac{\lambda }{2}\]
B) \[\lambda \]is greater than\[\frac{\lambda }{2}\]
C) \[\lambda \] is greater than \[\frac{\lambda }{2}\] but less than \[\lambda ,\]
D) \[\lambda \] is exactly equal to\[\frac{\lambda }{2}\]
Correct Answer: C
Solution :
Energy of photoelectron \[E=\frac{hc}{\lambda }-W\] \[\Rightarrow \] \[\frac{hc}{\lambda }=E+W\] ?(i) where W is the work function for the metal surface (constant). \[2E=\frac{hc}{\lambda }-W\] \[\Rightarrow \] \[\frac{hc}{\lambda }=2E+W\] ?(ii) Dividing Eq. (i) by Eq. (ii), we get \[\frac{\lambda }{\lambda }=\frac{E+W}{2E+W}\] \[\frac{\lambda }{\lambda }=\frac{(E+W)}{\left( E+\frac{W}{2} \right)}\] \[\therefore \] \[\frac{\lambda }{\lambda }>\frac{1}{2}\] or \[\lambda >\frac{\lambda }{2}\] \[\therefore \] \[\lambda >\lambda >\frac{\lambda }{2}\]
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